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Most of the common latin words are almost always used in an abbreviated form, even when the word is short, like id est -> i.e.. I can't picture anybody thinking that it would be ok to abbreviate "that is" to t.i or something like that.
Additionally why are some abbreviated in lower-case, but not all?
Examples i.e. e.g. MO (for some reason usually written like this :/) etc. id.
They are used because scribes were ever concerned with paper and ink. As English was first written in a formal alphabet by Latin educated scribes, Latin terms were ever present. Some were used so often, they came to be abbreviated to save time, and ink and paper. Paper was never really inexpensive until wood pulp became the principle material in the paper mills in the second half of the 19th Century. Before that, most paper was made from rags and virgin fiber that could be used for other purposes and the supply of all that was limited. Pre-Modern period, The best inks were also hard to come by. The availability of paper and ink was also subject the the lack of economies of production,i.e., paper and ink were not produced in any efficient manner, as the demand was small.
As scribes attempted to conserve writing materials as they could, abbreviations became normal. And that continued in the early days of moveable type, printers adopting the hand writer's norms. So, abbreviations continue to this day, as they have been and continue to be, normal in written English.
